Unit 2 Review: Logarithmic and Exponential Equations
Which table represents the graph of a logarithmic function in the form y = logbX when b > 1
A
Which graph represents an exponential function?
A (l-shaped)
For what value of a does 9 = (1/27)^a+3
A -11/3
What is the approximate value of x in the equation below. log3/4^25 = 3x - 1
A -3.396
For what value of a does (1/9)^a+1 = 81^a+1 * 27^2-a
A -4
A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = -2.78(log P) - 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.
A -5.95
If 8^y = 16^y+2, what is the value of y
A -8
Given log4^3 is approximately 0.792 and log 4^21 is approximately 2.196, what is log4^7?
A 1.404
Which logarithmic equation is equivalent to 8^2 = 64?
A 2 = log8^64
What is the product of (3y^-4)(2y^-4)
A 6/y^6
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10logl/l0, where l0 = 10^-12 and is the least intense sound a human ear can hear. Brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. The sound intensity level that Brandon can hear is 10^-10. Ahmad, Brandon's neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is 10^-4. How does Brandon's sound intensity level compare to Ahmad's mower?
A Brandon's sound intensity is 1/4 the level of Ahmad's mower.
A student solved the equation below by graphing. log6(x-1) = log2(2x+2) Which statement about the graph is true?
A The curves do not intersect.
What are the domain and range of f(x) = logx-5
A domain: x > 0; range: all real numbers
Which function represents a vertical stretch of an exponential function?
A f(x) = 3(1/2)^x
Which expression results when the change of base formula is applied to log4(x+2)?
A log(x+2)/log4
Which of the following is equivalent to log9w?
A log9 + logw
Which of the following is equivalent to log^(1/9)/k?
A log^1/9 - logk
Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a cannot equal 1 and b cannot equal 1? logaX
A logbX/logbA
Which statement best describes the domain and range of p(x) = 6^-x and q(x) = 6
A p(x) and q(x) have the same domain and the same range
Which of the following describes the transformations of g(x) = -2(2)^x+4 - 2 from the parent function f(x) = 2^x
A shift 4 units left, reflect over the x-axis, shift 2 units down
Which statement is true for log3(x+1) = 2?
A x + 1 = 3^2
Which of the following is the inverse of y = 6^x
A y = log6X
Consider the equation below. log4(x+3) = log2(2+x) Which system of equations can represent the equation?
A y1 = log(x+3)/log4 , y2 = log(2+x)/log2
Describe how (2^3)(2^-4) can be simplified
Add the exponents and keep the same base. Then find the reciprocal and change the sign of the exponent.
Tenisha solved the equation below by graphing a system of equations. log3^5x = log5(2x+8) Which point approximates the solution for Tenisha's system of equations?
B (1.0 , 1.4)
If 5^3b-1 = 5^b-3, what is the value of b
B -1
For what value of x does 4^x = (1/8)^x+5
B -3
What is the value of log 43? Use a calculator. Round your answer to the nearest tenth.
B 1.6
if 2^2x = 2^3, what is the value of x
B 3/2
If 36^12-m = 6^2m, what is the value of m
B 6
What are the domain and range of f(x) = (1/5)^x
B The domain is all real numbers. The range is all real numbers greater than zero.
The table shows a student's proof of the quotient rule for logarithms. Let M = b^x and N = b^y for some real numbers x and y. What is the error in the proof?
B The error is in step 3. You cannot use a property of logarithms to prove that the same property.
What are the domain and range of the function f(x) = 3^x + 5
B domain: (-infinity,infinity); range: (5,infinity)
What are the domain and range of f(x) = log(x+6)-4
B domain: x > -6; range: all real numbers
Which statement best describes the domain and range of f(x) = -(7)^x and g(x) = 7^x
B f(x) and g(x) have the same domain but different ranges
Which expression is equivalent to log12((1/2)/8w)?
B log12^1/2-(log12^8+log12^W)
Tyler applied the change of base formula to a logarithmic expression. The resulting expression is shown below. (log1/4)/log12 Which expression could be Tyler's original expression?
B log12^1/4
What is 2(log3^8+log3^Z) - log3(3^4-7^2) written as a single logarithm?
B log3^2z^2
What is 2log5(5x^3) + 1/3log5(x^2+6) written as a single logarithm?
B log5(25x^6)3 squareroot of x^2 + 6
Which expression is equivalent to log8^4a(b-4/c^4)?
B log8^4 + log8^A + (log8(b-4)-4log8^C)
What is the solution to log2(2x^3-8) - 2log2^X = log2^X?
B x = 2
What is the solution to log2(9x) - log2^3 = 3?
B x = 8/3
Which equation is equivalent to logx^36 = 2
B x^2 = 36
Which function is graphed below?
B y = 3(1/3)^x
Which of the following is the inverse of y = 3^x
B y = log3X
Which system of equations could be graphed to solve the equation below? log(2x+1) = 3x-2
B y1 = log(2x+1) , y2 = 3x-2
Which set of ordered pairs could be generated by an exponential function?
C (-1,1/2) , (0,1) , (1,2) , (2,4)
Which set of ordered pairs could be generated by an exponential function
C (1,1/2) , (2,1/4) , (3,1/8) , (4,1/16)
What is the approximate value of q in the equation below? q + log2^6 = 2q + 2
C 0.585
What is the value of log 13? Use a calculator. Round your answer to the nearest tenth
C 1.1
Kim solved the equation below by graphing a system of equations. log2(3x-1) = log4(x+8) What is the approximate solution to the equation?
C 1.4
Which expression is equivalent to (10x)^-3
C 1/1000x^3
Which expression is equivalent to (3^2)^-2
C 1/81
Which expression is equivalent to 9^-2
C 1/81
Given log3^2 is approximately 0.631 and log 3^7 is approximately 1.771, what is log3^14?
C 2.402
What is the value of log27^9
C 2/3
Which equation is equivalent to log3(x+5) = 2
C 3^2 = x + 5
If 3^2x+1 = 3^x+5, what is the value of x
C 4
What is the value of log3^81
C 4
Which expression is equivalent to 5y^-3
C 5/y^3
What is the quotient of 7^-1/7^-2
C 7
Which properties are present in a table that represents a logarithmic function in the form y = logbX when b > 1 I. The y-values are always increasing or always decreasing. II. The point (0, 1) exists in the table. III. The y-values will decrease rapidly as the x-values approach zero. IV. There will only be one x-value in the table with a y-value of zero.
C I, III, and IV
Anja simplified the expression 10x^-5/-5x10 to 15/x^15. What mistake did Anja make
C She subtracted the coefficients instead of dividing them
Which statement is true
C The graph of y = logb(X)+4 is the graph of y = logb(X) translated 4 units up
Which logarithmic equation has the same solution as x-4 = 2^3?
C log2(x-4) = 3
Which expression is equivalent to log3(x+4)?
C log3 + log(x+4)
Which expression is equivalent to log3^c/9
C log3c - log3(9)
Sam is proving the product property of logarithms. Which expression and justification completes the third step of her proof?
C logb(b^x+y); power rule of exponents
The proof for the power property of logarithms appears in the table with an expression missing. (step 3/6) Which expression is missing from the proof?
C logb(b^xy)
Which of the following shows the extraneous solution to the logarithmic equation? log4(x) + log4(x-3) = log4(-7x+21)
C x = 3 and x = -7
Which of the following is true regarding the solutions to the logarithmic equation below? 2log6(x) = 2 log6(x^2) = 2 x^2 = 6^2 x^2 = 36 x = 6 , -6
C x = 6 is a true solution and x = -6 is an extraneous solution
Which function has a range of y < 3
C y = -(2)^x + 3
Which of the following exponential equations could be represented by the table below?
C y = 3^x-3 + 2
Which of the following is a logarithmic function?
C y = log0.25X
Which statement is true
C y = log1X is not a logarithmic function because the base is equal to 1
Which function is shown in the graph below
C y = log3X
Which set of ordered pairs could be generated by an exponential function
D (0,1) , (1,3) , (2,9) , (3,27)
Which graph represents an exponential function?
D (upside down l-shaped)
For what value of y does 125 = (1/25)^y-1
D -1/2
What is the quotient of -8x^6/4x^-3
D -2x^9
Which expression is equivalent to 5y^3/(5y)^-2
D 125y^5
What is the quotient of 2^4/2^-4
D 256
What is the value of log7^343
D 3
What is log15^2^3 rewritten using the power property?
D 3log15^2
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10logl/l0, where l0 = 10^-12 and is the least intense sound a human ear can hear. What is the approximate loudness of a dinner conversation with a sound intensity of 10^-7?
D 50 Db
For what value of b does (1/12)^-2b * 12^-2b+2 = 12
D No solution
Sebastian used the table and correctly identified that the data does not represent a logarithmic function. What information did Sebastian use in his deduction?
D The table shows two x-intercepts and it changes from increasing to decreasing
Devonte used the change of base formula to approximate log8^25. Which expression did Devonte use?
D log25/log8
Which equation has x = -6 as the solution?
D log3(-2x-3) = 2
What is log5(4*7) + log5^2 written as a single log?
D log5^56
When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used. Which property listed below is used in all of these proofs?
D logb(b^y) = y
Which is equivalent to log2^17 = 4?
D logn = 4log2
Which of the following describes the transformation of g(x) = 3(2)^-x + 2 from the parent function f(x) = 2^x
D reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up
What is the solution to log5(10x-1) = log5(9x+7)?
D x = 8
Which function is shown in the graph below
D y = log6X
Which system of equations could be graphed to solve the equation below? log0.5X = log3^2 + x
D y1 = logx/log0.5 , y2 = log2/log3 + x
Omar wants to use a graph to solve the equation below. log6X = log2(x+4) Which system of equations should Omar use?
D y1 = logx/log6 , y2 = log(x+4)/log2
Describe how to simplify the expression 3^-6/3^-4
Keep the base the same and then subtract the exponents
Which expression is equivalent to 6^-3
(1/6)^3
How can you use transformations to graph this function? y = 3 * 7^-x + 2
*Sketch the graph of y = 7^x *Reflect the graph across the y-axis to show the function y = 7^-x *Stretch the graph vertically by a factor of 3 to show the function y = 3 * 7^-x *Shift the graph up 2 units to show the function y = 3 * 7^-x + 2
